Problem: Solve for $x$ and $y$ using elimination. ${-4x-6y = -78}$ ${x-5y = -39}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the bottom equation by $4$ ${-4x-6y = -78}$ $4x-20y = -156$ Add the top and bottom equations together. $-26y = -234$ $\dfrac{-26y}{{-26}} = \dfrac{-234}{{-26}}$ ${y = 9}$ Now that you know ${y = 9}$ , plug it back into $\thinspace {-4x-6y = -78}\thinspace$ to find $x$ ${-4x - 6}{(9)}{= -78}$ $-4x-54 = -78$ $-4x-54{+54} = -78{+54}$ $-4x = -24$ $\dfrac{-4x}{{-4}} = \dfrac{-24}{{-4}}$ ${x = 6}$ You can also plug ${y = 9}$ into $\thinspace {x-5y = -39}\thinspace$ and get the same answer for $x$ : ${x - 5}{(9)}{= -39}$ ${x = 6}$